Transmit beamforming (sometimes referred to as transmit adaptive array (TXAA) transmission) increases the effective signal-to-noise ratio seen by a receiver device by creating a coverage pattern that tends to be directional in nature (i.e., not uniformly broadcast). Transmit beamforming is accomplished by employing multiple antennas at the transmit site and weighting each antenna such that the combined transmissions result in a beamformed pattern that delivers maximum power/energy to the receiver.
In the implementation of the transmit and receive radio frequency (RF) hardware, an unknown gain and phase is present on each transmit and receive branches due to such hardware mismatches such as cable length differences and filter response differences. These unknown gain and phase values, which may be frequency selective, make direction of arrival (DOA) or direction of departure (DOD) estimation difficult (if not impossible) because they cause the baseband array response vector for a given DOA or DOD to be different from what would be predicted from the array geometry (i.e., the position and orientation of the antennas comprising the antenna array).
Fortunately these gain and phase values change slowly in time (typically on the order of hours), so they can be estimated and their effects removed from the received or transmitted signals during manifold calibration. For DOD beamforming, manifold calibration means that for each DOD of interest, the corresponding transmit array response vector at baseband corresponds (to within a scalar constant) to the array response vector that would be predicted from the array geometry. If the array is manifold calibrated, then a DOA estimated on the uplink can easily be translated to a DOD on the downlink (i.e., a beam can be pointed in the mobile direction using an uplink DOA estimate). For DOA estimation on the uplink, manifold calibration means that the baseband response of a signal received from a certain direction on the uplink matches the array response vector predicted from the array geometry (or equivalently that the baseband vector channel response is spatially equivalent to the RF vector channel response).
FIG. 1 illustrates gain and phase values introduced by system hardware. First, the response of the base station transmit hardware from baseband to RF is captured by the M×1 vector q(k) where M is the number of antennas (transmit and receive) at the base station and k is the subcarrier (or frequency) index. Similarly, the response of the base station receiver hardware from RF to baseband is captured by the M×1 vector g(k). In the figure, g1(k) refers to element one of g(k), g2(k) refers to element 2 of g(k), and so on (and a similar definition is true for q(k)).
In an OFDM communication system, the M×1 noiseless signal received at the base station array of M antennas from a mobile with a single antenna may be modeled at baseband in the frequency domain as
                              M          ×          1          ⁢                                          ⁢                      Y            ⁡                          (                              k                ,                b                            )                                      =                              x            ⁡                          (                              k                ,                b                            )                                ⁢                                    ∑                              l                =                1                            P                        ⁢                                                            γ                  l                                ⁡                                  (                  b                  )                                            ⁢                              G                ⁡                                  (                  k                  )                                            ⁢                              a                ⁡                                  (                                      θ                    l                                    )                                            ⁢                              ⅇ                                                      -                    j                                    ⁢                                                                          ⁢                  2                  ⁢                  π                  ⁢                                                                          ⁢                  k                  ⁢                                                                          ⁢                                      τ                    l                                    ⁢                                      Δ                    F                                                                                                          (        1        )            where k is the subcarrier index, b is the time (OFDM symbol) index, x(k,b) is the transmitted symbol, P is the number of multipath components (rays), γl(b) is the complex gain of the lth multipath component, G(k)=diag(g1(k), . . . , gM(k)) where gm(k) is the receive hardware induced gain and phase for receive antenna m, τl is the time of arrival (TOA) for path l, ΔF is the subcarrier separation (in Hz), θl is the DOA of the lth path, and a(θ) is the array manifold vector which for a uniform linear array with inter-element spacing of d (in wavelengths) is given as
                              M          ×          1          ⁢                                          ⁢                      a            ⁡                          (              θ              )                                      =                              [                                                            1                                                                                                  ⅇ                                                                  -                        j                                            ⁢                                                                                          ⁢                      2                      ⁢                      π                      ⁢                                                                                          ⁢                                              dsin                        ⁡                                                  (                          θ                          )                                                                                                                                                                  ⋮                                                                                                  ⅇ                                                                  -                        j                                            ⁢                                                                                          ⁢                      2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                                              d                        ⁡                                                  (                                                      M                            -                            1                                                    )                                                                    ⁢                                                                                          ⁢                      s                      ⁢                                                                                          ⁢                      i                      ⁢                                                                                          ⁢                                              n                        ⁡                                                  (                          θ                          )                                                                                                                                          ]                    .                                    (        2        )            The goal of DOA calibration is to find a matrix C(k)=diag(c1(k), . . . , cM(k)), which contains the DOA calibration coefficients, that when it is applied to Y(k,b), removes the effects of G(k). Mathematically the application of C(k) can be expressed as:
                                          Y            ~                    ⁡                      (                          k              ,              b                        )                          =                                            C              ⁡                              (                k                )                                      ⁢                          Y              ⁡                              (                                  k                  ,                  b                                )                                              =                                    x              ⁡                              (                                  k                  ,                  b                                )                                      ⁢                                          ∑                                  l                  =                  1                                P                            ⁢                                                                    γ                    l                                    ⁡                                      (                    b                    )                                                  ⁢                                  a                  ⁡                                      (                                          θ                      l                                        )                                                  ⁢                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    k                    ⁢                                                                                  ⁢                                          τ                      l                                        ⁢                                          Δ                      F                                                                                                                              (        3        )            which now has the unknown receiver gains and phases removed and thus a ray from angle θl will appear to mathematically match the array response vector in Error! Reference source not found. This type of DOA calibration is shown in FIG. 2 where additional blocks are included on the input to each receive branch (ci(k)). These blocks represent the calibration coefficients that are applied to eliminate the effects of G(k).
On the transmit side, the transmitted signal from the M-element base array received at a single mobile antenna may be modeled as:
                              z          ⁡                      (                          k              ,              b                        )                          =                                            v              T                        ⁡                          (                              k                ,                b                            )                                ⁢                                    ∑                              l                =                1                            P                        ⁢                                                            γ                  l                                ⁡                                  (                  b                  )                                            ⁢                              Q                ⁡                                  (                  k                  )                                            ⁢                              a                ⁡                                  (                                      θ                    l                                    )                                            ⁢                              ⅇ                                                      -                    j                                    ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  k                  ⁢                                                                          ⁢                                      τ                    l                                    ⁢                                      Δ                    F                                                                                                          (        4        )            where v(k,b) is a M×1 vector containing the frequency-domain signals transmitted from each transmit antenna and Q(k)=diag(q1(k), . . . , qM(k)) where qm(k) is the transmit hardware induced gain and phase for transmit antenna m. Note that some of the downlink channel parameters will be the same as the uplink channel in Error! Reference source not found. such as the angles (the DODs equal the DOAs) and the TOAs regardless of whether the system is time division duplexed (TDD) or frequency division duplexed (FDD). However, for FDD systems, the channel gains and antenna spacing in wavelengths will be different on the uplink and downlink, whereas for TDD systems the channel gains are likely the same on the uplink and downlink. The transmitted frequency-domain signal from each antenna, v(k,b), can be pilot sequences which enable mobiles to compute the downlink channel. This measured downlink channel can then be turned into feedback (e.g., codebook feedback) which the mobile will send to the base station. This feedback can be used by the base to beamform the downlink. Another example of v(k,b) is DOD beamforming with v(k,b)=wx(k,b) where x(k,b) is a data stream and w is an M×1 vector corresponding to the DOD beamformer as is known in the art.
The goal of DOD calibration is to estimate a matrix D(k)=diag(d1(k), . . . , dM(k)), which contains the DOD calibration coefficients, that when applied to the transmitted signal will remove the effects of Q(k). The DOD calibration is illustrated in FIG. 2 where the output from each transmit branch has DOD calibration coefficient (dm(k) for antenna branch m) applied. Mathematically the DOD calibrated signal is given as
                                                                                          z                  ~                                ⁡                                  (                                      k                    ,                    b                                    )                                            =                                                                    v                    T                                    ⁡                                      (                                          k                      ,                      b                                        )                                                  ⁢                                                      ∑                                          l                      =                      1                                        P                                    ⁢                                                                                    γ                        l                                            ⁡                                              (                        b                        )                                                              ⁢                                          Q                      ⁡                                              (                        k                        )                                                              ⁢                                          a                      ⁡                                              (                                                  θ                          l                                                )                                                              ⁢                                          ⅇ                                                                        -                          j                                                ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                        k                        ⁢                                                                                                  ⁢                                                  τ                          l                                                ⁢                                                  Δ                          F                                                                                                                                                                                            =                                                                    v                    T                                    ⁡                                      (                                          k                      ,                      b                                        )                                                  ⁢                                                      ∑                                          l                      =                      1                                        P                                    ⁢                                                                                    γ                        l                                            ⁡                                              (                        b                        )                                                              ⁢                                          a                      ⁡                                              (                                                  θ                          l                                                )                                                              ⁢                                          ⅇ                                                                        -                          j                                                ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                        k                        ⁢                                                                                                  ⁢                                                  τ                          l                                                ⁢                                                  Δ                          F                                                                                                                                                                            (        5        )            which has the effects of the transmit hardware removed.
As mentioned above v(k,b) could be traditional DOD beamforming based on an estimate of the DOA on the uplink.
The existing manifold calibration methods either require special hardware at the base station like calibration hardware or a sensing antenna or require hardware outside of the base station like a special transceiver with a fixed location to perform calibration. Hence a need exists for a method and apparatus for determining the appropriate calibration coefficients in software without the need of special calibration equipment at the base or by needing a dedicated fixed transceiver for calibration.
Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions and/or relative positioning of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of various embodiments of the present invention. Also, common but well-understood elements that are useful or necessary in a commercially feasible embodiment are often not depicted in order to facilitate a less obstructed view of these various embodiments of the present invention. It will further be appreciated that certain actions and/or steps may be described or depicted in a particular order of occurrence while those skilled in the art will understand that such specificity with respect to sequence is not actually required. Those skilled in the art will further recognize that references to specific implementation embodiments such as “circuitry” may equally be accomplished via replacement with software instruction executions either on general purpose computing apparatus (e.g., CPU) or specialized processing apparatus (e.g., DSP). It will also be understood that the terms and expressions used herein have the ordinary technical meaning as is accorded to such terms and expressions by persons skilled in the technical field as set forth above except where different specific meanings have otherwise been set forth herein.